CN110568144B - Temperature compensation method for ammonia nitrogen detection - Google Patents

Temperature compensation method for ammonia nitrogen detection Download PDF

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CN110568144B
CN110568144B CN201910931224.7A CN201910931224A CN110568144B CN 110568144 B CN110568144 B CN 110568144B CN 201910931224 A CN201910931224 A CN 201910931224A CN 110568144 B CN110568144 B CN 110568144B
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ammonia nitrogen
temperature
formula
temperature compensation
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苏成志
盛宇博
姜吉光
王恩国
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Changchun University of Science and Technology
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Abstract

A temperature compensation method for ammonia nitrogen detection belongs to the technical field of water quality detection, and aims to solve the problem that temperature compensation errors are large in a low-temperature environment when temperature compensation is performed only on a sensor, and the method comprises the following steps: step one, establishing a functional relation between z (x, y) and x and y: acquiring output readings of ammonia nitrogen detected by the sensors at different temperatures; step three, determining an objective function of z (x, y): step four, solving the optimal solution of the function coefficient established in the step one
Figure DDA0002218157930000011
Step five, establishing a temperature compensation model; the method utilizes a mathematical optimization technology to establish a fusion ammonia nitrogen temperature compensation model about an ammonia nitrogen water sample and an ammonia nitrogen sensor. The model has good compensation effect on low-temperature environment detection, can compensate the ammonia nitrogen concentration at a certain temperature into the ammonia nitrogen concentration value at the standard temperature (20 ℃), can realize secondary correction on the model through changing temperature experiment data so as to improve the precision of the model, and has high compensation precision.

Description

Temperature compensation method for ammonia nitrogen detection
Technical Field
The invention relates to the technical field of water quality detection, in particular to a temperature compensation method for ammonia nitrogen detection.
Background
In recent years, excessive discharge of ammonia nitrogen has gradually become a main factor of most river pollution in China, and an ammonia nitrogen sensor based on an electrochemical method has the characteristics of convenience in carrying, rapidness and high efficiency in detection and the like, and is widely applied to field water quality online monitoring. According to the Nernst theory, temperature change can affect the response of the ammonia nitrogen sensor, and the detection of the ammonia nitrogen sensor can be obviously interfered when the outdoor water temperature is generally changed from 0 ℃ to 35 ℃.
Aiming at the problem of interference of temperature change on ammonia nitrogen detection, a paper entitled "ammonia nitrogen online detector compensation model based on ammonia-sensitive electrode" is published in journal "analysis laboratory" by Wu Shi Guang et al, the paper only explores the influence of temperature on a sensor according to the theoretical principle of an ammonia nitrogen sensor, deduces a theoretical temperature compensation method through an Nernst equation and compensates the temperature of the sensor, but in the field actual detection process, the change of temperature not only influences the sensor, but also influences the existence form of ammonia nitrogen in water, and particularly influences the existence form of ammonia nitrogen in a low-temperature environment (0-20 ℃) are more obvious. Therefore, the problem of large compensation error in low-temperature environment exists when the temperature of the sensor is compensated by the prior art.
Disclosure of Invention
The invention provides a method for processing ammonia nitrogen experimental data through a mathematical optimization technology to establish an ammonia nitrogen temperature compensation model, aiming at solving the problem of large temperature compensation error in a low-temperature environment when only a sensor is subjected to temperature compensation. The temperature compensation can be simultaneously carried out on the water sample and the sensor through the data fusion processing of the output value of the ammonia nitrogen sensor, the standard value of the ammonia nitrogen solution and the temperature, and the method can compensate the ammonia nitrogen concentration at a certain temperature to the ammonia nitrogen concentration at the standard temperature (20 ℃) in real time.
The technical scheme adopted by the invention is as follows:
the low-temperature compensation method for ammonia nitrogen detection is characterized by comprising the following steps of:
step one, establishing a functional relation between z (x, y) and x and y:
z(x，y)＝a0+a1x+a2y+a3x2+a4xy+a5y2+a6x3+a7x2y+a8xy2+a9y3 (1)；
in formula (1): x represents the sample temperature, y represents the output reading of the ammonia nitrogen sensor, z (x, y) represents the standard concentration of ammonia nitrogen at the standard temperature, a0,a1,…a9Is a coefficient of formula (1);
acquiring output readings of ammonia nitrogen detected by the sensors at different temperatures;
detecting ammonia nitrogen samples with different standard concentrations at different temperatures by using an ammonia nitrogen sensor to obtain n groups of ammonia nitrogen detection records as (x)i，yi，zi)，i＝1，2，3…n，xi∈x、yi∈y、zi∈z(x，y)；
Step three, determining an objective function of z (x, y):
Figure BDA0002218157910000021
in the formula (2)
Figure BDA0002218157910000022
Is a in the formula (1)0、a1，…a9The optimal solution of (2);
step four, solving the optimal solution of the coefficient of the formula (1)
Figure BDA0002218157910000023
Solving equation (2) by least squares method, it is necessary to
Figure BDA0002218157910000024
Satisfies formula (3):
Figure BDA0002218157910000025
solving the formula (3) to obtain:
Figure BDA0002218157910000026
in formula (4):
Figure BDA0002218157910000027
b＝(z1，z2，...，zn)T (6)；
step five, establishing a temperature compensation model;
coefficient obtained by equation (4)
Figure BDA0002218157910000028
Substituting into formula (1) to obtain:
Figure BDA0002218157910000029
the invention has the beneficial effects that: a fusion ammonia nitrogen temperature compensation model about an ammonia nitrogen water sample and an ammonia nitrogen sensor is established by using a mathematical optimization technology. The model has good compensation effect on low-temperature environment detection, can compensate the ammonia nitrogen concentration at a certain temperature into the ammonia nitrogen concentration value at the standard temperature (20 ℃), can realize secondary correction on the model through changing temperature experiment data so as to improve the precision of the model, and has high compensation precision. The temperature compensation can be performed on ammonia nitrogen sensors of different types and brands by fusing data layers only by modifying related experimental data, and the universality is high.
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FIG. 1: the invention relates to a flow chart of a temperature compensation method for ammonia nitrogen detection.
FIG. 2: the temperature experiment of the invention acquires a sample point distribution diagram.
FIG. 3: the invention discloses a three-dimensional schematic diagram of a temperature compensation model.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings.
The invention provides a method for processing ammonia nitrogen experimental data through a mathematical optimization technology to establish an ammonia nitrogen temperature compensation model, aiming at solving the problem of large temperature compensation error in a low-temperature environment when only a sensor is subjected to temperature compensation. The temperature compensation can be simultaneously carried out on the water sample and the sensor through the data fusion processing of the output value of the ammonia nitrogen sensor, the standard value of the ammonia nitrogen solution and the temperature, and the method can compensate the ammonia nitrogen concentration at a certain temperature to the ammonia nitrogen concentration at the standard temperature (20 ℃) in real time.
As shown in fig. 1, a temperature compensation method for ammonia nitrogen detection comprises the following steps:
step one, establishing a functional relation between z (x, y) and x and y;
x represents the sample temperature, y represents the output reading of the ammonia nitrogen sensor, and z (x, y) represents the standard concentration of ammonia nitrogen at the standard temperature.
(x，y)＝a0+a1x+a2y+a3x2+a4xy+a5y2+a6x3+a7x2y+a8xy2+a9y3 (1)；
Wherein a is0,a1,…a9Is the coefficient of formula (1);
acquiring output readings of ammonia nitrogen detected by the sensors at different temperatures;
detecting ammonia nitrogen samples with different standard concentrations at different temperatures by using an ammonia nitrogen sensor to obtain n groups of ammonia nitrogen detection records as (x)i，yi，zi)，i＝1，2，3…n，xi∈x、yi∈y、zi∈z。
As shown in fig. 2, a sample point distribution diagram is acquired in the temperature experiment;
step three, determining an objective function about z (x, y):
Figure BDA0002218157910000031
Figure BDA0002218157910000032
is about unknown numbers
Figure BDA0002218157910000033
An objective function of, wherein
Figure BDA0002218157910000034
Is a in the formula (1)0，a1，…a9The optimal solution of (2);
step four, solving the optimal solution of the coefficient of the formula (1)
Figure BDA0002218157910000041
Solving equation (2) by least squares method, it is necessary to
Figure BDA0002218157910000042
Satisfies formula (3):
Figure BDA0002218157910000043
solving the formula (3) to obtain:
Figure BDA0002218157910000044
in formula (4):
Figure BDA0002218157910000045
b＝(z1，z2，...zn)T (6)；
step five, establishing a temperature compensation model;
and (4) carrying the experimental data measured in the step two into the formula (4):
Figure BDA0002218157910000046
coefficient obtained by equation (4)
Figure BDA0002218157910000047
Substituting into formula (1) to obtain:
z＝0.9673-0.088x+1.287y+0.00551x2-0.01195xy-0.001303y2-0.0001536x3-
1.979×10-5x2y-3.686×10-5y2x+1.993×10-5y3
(7)。
as shown in fig. 3, the temperature compensation model is a three-dimensional schematic diagram;
and (3) detecting the output reading of the water sample to be detected and the temperature of the water sample by the recording sensor, and substituting the data into the temperature compensation model (7) so as to obtain a compensated value, namely the true ammonia nitrogen content of the water sample. For example: when the temperature of a water sample is 5 ℃, the output readout of the ammonia nitrogen sensor is 3.7mg/L, namely x is 5, y is 3.7, and x and y are substituted into formula (7) to obtain the ammonia nitrogen concentration z which is 5.06 at the standard temperature (20 ℃).
The accuracy verification of the ammonia nitrogen temperature compensation model is to carry out the temperature experiment on the ammonia nitrogen reagent with random concentration, bring the experimental data into the temperature compensation model for compensation, and utilize the formula: the fitting error (%) (accuracy) ═ estimated mass concentration-actual mass concentration |/actual mass concentration × 100%, the verification data obtained are shown in table 1;
TABLE 1
Figure BDA0002218157910000051
From table 1, the maximum relative error after compensation is 3.0%, the minimum relative error is-0.20%, and the errors are within ± 3%, which shows that the temperature compensation model has good compensation accuracy.
Substituting into the average deviation formula:
Figure BDA0002218157910000052
wherein,
Figure BDA0002218157910000053
represents the mean deviation; sigmaiError representing a single term determination; n represents the number of measurements;
Figure BDA0002218157910000054
represents the average of n measurement errors;
Figure BDA0002218157910000055
represents the absolute deviation of the individual measurement from the mean;
calculating the mean deviation
Figure BDA0002218157910000056
The small average deviation shows that the temperature compensation effect of the model is good.

Claims (1)

1. A low-temperature compensation method for ammonia nitrogen detection is characterized by comprising the following steps:
step one, establishing a functional relation between z (x, y) and x and y:
z(x，y)＝a0+a1x+a2y+a3x2+a4xy+a5y2+a6x3+a7x2y+a8xy2+a9y3 (1)；
in formula (1): x represents the sample temperature, y represents the output reading of the ammonia nitrogen sensor, z (x, y) represents the standard concentration of ammonia nitrogen at the standard temperature, a0,a1,…a9Is a coefficient of formula (1);
acquiring output readings of ammonia nitrogen detected by the sensors at different temperatures;
detecting ammonia nitrogen samples with different standard concentrations at different temperatures by using an ammonia nitrogen sensor to obtain n groups of ammonia nitrogen detection records as (x)i，yi，zi)，i＝1,2,3…n，xi∈x、yi∈y、zi∈z(x，y)；
Step three, determining an objective function of z (x, y):
Figure FDA0002218157900000011
in the formula (2)
Figure FDA0002218157900000012
Is a in the formula (1)0、a1,…a9The optimal solution of (2);
step four, solving the optimal solution of the coefficient of the formula (1)
Figure FDA0002218157900000013
Solving equation (2) by least squares method, it is necessary to
Figure FDA0002218157900000014
(k is 0, 1 … 9) satisfies formula (3):
Figure FDA0002218157900000015
solving the formula (3) to obtain:
Figure FDA0002218157900000016
in formula (4):
Figure FDA0002218157900000017
b＝(z1，z2，...，zn)T (6)；
step five, establishing a temperature compensation model;
coefficient obtained by equation (4)
Figure FDA0002218157900000021
Substituting into formula (1) to obtain:
Figure FDA0002218157900000022
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